Uniqueness of spaces pretangent to metric spaces at infinity

Uniqueness of spaces pretangent to metric spaces at infinity

We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It...

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Published in:Український математичний вісник
Date:2019
Main Authors: Dovgoshey, O., Bilet, V.
Format: Article
Language:Russian
Published: Інститут прикладної математики і механіки НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/169432
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-169432
record_format dspace
spelling Dovgoshey, O.
Bilet, V.
2020-06-13T08:23:45Z
2020-06-13T08:23:45Z
2019
Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ.
1810-3200
2010 MSC. 54E35
https://nasplib.isofts.kiev.ua/handle/123456789/169432
We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It is also shown that the uniqueness of pretangent spaces to subsets of a real line is closely related to the “asymptotic asymmetry” of these subsets.
ru
Інститут прикладної математики і механіки НАН України
Український математичний вісник
Uniqueness of spaces pretangent to metric spaces at infinity
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Uniqueness of spaces pretangent to metric spaces at infinity
spellingShingle Uniqueness of spaces pretangent to metric spaces at infinity
Dovgoshey, O.
Bilet, V.
title_short Uniqueness of spaces pretangent to metric spaces at infinity
title_full Uniqueness of spaces pretangent to metric spaces at infinity
title_fullStr Uniqueness of spaces pretangent to metric spaces at infinity
title_full_unstemmed Uniqueness of spaces pretangent to metric spaces at infinity
title_sort uniqueness of spaces pretangent to metric spaces at infinity
author Dovgoshey, O.
Bilet, V.
author_facet Dovgoshey, O.
Bilet, V.
publishDate 2019
language Russian
container_title Український математичний вісник
publisher Інститут прикладної математики і механіки НАН України
format Article
description We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It is also shown that the uniqueness of pretangent spaces to subsets of a real line is closely related to the “asymptotic asymmetry” of these subsets.
issn 1810-3200
url https://nasplib.isofts.kiev.ua/handle/123456789/169432
citation_txt Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ.
work_keys_str_mv AT dovgosheyo uniquenessofspacespretangenttometricspacesatinfinity
AT biletv uniquenessofspacespretangenttometricspacesatinfinity
first_indexed 2025-11-30T13:44:32Z
last_indexed 2025-11-30T13:44:32Z
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